Problem: Divide the polynomials. The form of your answer should either be $p(x)$ or $p(x)+\dfrac{k}{x+3}$ where $p(x)$ is a polynomial and $k$ is an integer. $\dfrac{2x^3-x^2-25x-12}{x+3}=$
Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} 2x^2-\phantom{1}7x-\phantom{1}4 \\ x+3|\overline{2x^3-\phantom{6}x^2-25x-12} \\ \mathllap{-(}\underline{2x^3+6x^2\phantom{-28x-12}\rlap )} \\ -7x^2-25x-12 \\ \mathllap{-(}\underline{-7x^2-21x\phantom{-12}\rlap )} \\ -4x-12 \\ \mathllap{-(}\underline{-4x-12\rlap )} \\ 0 \end{array}$ We found that the quotient is $2x^2-7x-4$ and the remainder is $0$, which means the answer is simply a polynomial (no expression of the form $\dfrac{k}{x+3}$ ). $\dfrac{2x^3-x^2-25x-12}{x+3}=2x^2-7x-4$